Answered: Consider a First-Order Logic (FOL)…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Consider a First-Order Logic (FOL) language L with two unary predicate symbols P and Q, one unary function f, and two constants a and b. The following KB has been specified in this language (note that I use directly "for all" to stand for the logical quantifier of "for-all").

1. (forall x)(Q(x) -> P(x)) (Note: the sentence is logically equivalent to (forall x) (~ Q(x) \/ P(x))).
2. P(b)
3. Q(b)

4. Q(f(a))

5. P(f(b))

Consider an interpretation of <D, I>, where D={d1, d2, d3}, and d1 is denoted by a, d2 is denoted b. For the function f, I(f,d1)=d2, I(f,d2)=d3, I(f,d3)=d1. and I(P)={d1, d2}, I(P)={d1, d2}. Is this interpretation a model of L?

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